Topological properties of solution sets for nonlinear evolution hemivariational inequalities and applications

Abstract

The purpose of this paper is to investigate the topological properties of solution sets for a class of nonlinear evolution hemivariational inequalities. We firstly obtain the nonemptiness and the compactness of the solution set for hemivariational inequalities by applying the Kakutani–KyFan fixed point theorem, Gronwall’s inequality and the multivalued analysis. Then by using Hyman’s theorem, we show that the solution set for presented problem is an Rδ set. Finally, some applications to infinite dimensional control systems are given.